Basic knowledge of the topics covered by the course:
Decompositions of signed measures, conditional expectations,
martingale theory, CLT for martingales, and definition, existence
and path properties of the Brownian motion.

Skill:

describe and prove the results on decomposition of signed
measures.

use the calculation rules for conditional expectations.

show whether a sequence of random variables is a martingale or
a submartingale.

derive and describe the main results on martingales.

apply the results on martingales to concrete examples.

describe the foundation for the construction of stochastic
processes in continuous time.

describe the basic properties of the sample paths for Brownian
motion.

Competence:

discuss the relation between decomposition of measures and
conditional expectations.

relate and compare the results on martingales.

use martingale CLT and understand the result compared to the
classical CLT.

discuss the concept of sample paths with a view to constructing
continuous stochastic processes.

Give an oral presentation of a specific topic within the theory
covered by the course.